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Simplifying 3 = 0.014x2 + -1.19x + 25.24 Reorder the terms: 3 = 25.24 + -1.19x + 0.014x2 Solving 3 = 25.24 + -1.19x + 0.014x2 Solving for variable 'x'. Combine like terms: 3 + -25.24 = -22.24 -22.24 + 1.19x + -0.014x2 = 25.24 + -1.19x + 0.014x2 + -25.24 + 1.19x + -0.014x2 Reorder the terms: -22.24 + 1.19x + -0.014x2 = 25.24 + -25.24 + -1.19x + 1.19x + 0.014x2 + -0.014x2 Combine like terms: 25.24 + -25.24 = 0.00 -22.24 + 1.19x + -0.014x2 = 0.00 + -1.19x + 1.19x + 0.014x2 + -0.014x2 -22.24 + 1.19x + -0.014x2 = -1.19x + 1.19x + 0.014x2 + -0.014x2 Combine like terms: -1.19x + 1.19x = 0.00 -22.24 + 1.19x + -0.014x2 = 0.00 + 0.014x2 + -0.014x2 -22.24 + 1.19x + -0.014x2 = 0.014x2 + -0.014x2 Combine like terms: 0.014x2 + -0.014x2 = 0.000 -22.24 + 1.19x + -0.014x2 = 0.000 Begin completing the square. Divide all terms by -0.014 the coefficient of the squared term: Divide each side by '-0.014'. 1588.571429 + -85x + x2 = 0 Move the constant term to the right: Add '-1588.571429' to each side of the equation. 1588.571429 + -85x + -1588.571429 + x2 = 0 + -1588.571429 Reorder the terms: 1588.571429 + -1588.571429 + -85x + x2 = 0 + -1588.571429 Combine like terms: 1588.571429 + -1588.571429 = 0.000000 0.000000 + -85x + x2 = 0 + -1588.571429 -85x + x2 = 0 + -1588.571429 Combine like terms: 0 + -1588.571429 = -1588.571429 -85x + x2 = -1588.571429 The x term is -85x. Take half its coefficient (-42.5). Square it (1806.25) and add it to both sides. Add '1806.25' to each side of the equation. -85x + 1806.25 + x2 = -1588.571429 + 1806.25 Reorder the terms: 1806.25 + -85x + x2 = -1588.571429 + 1806.25 Combine like terms: -1588.571429 + 1806.25 = 217.678571 1806.25 + -85x + x2 = 217.678571 Factor a perfect square on the left side: (x + -42.5)(x + -42.5) = 217.678571 Calculate the square root of the right side: 14.753934086 Break this problem into two subproblems by setting (x + -42.5) equal to 14.753934086 and -14.753934086.Subproblem 1
x + -42.5 = 14.753934086 Simplifying x + -42.5 = 14.753934086 Reorder the terms: -42.5 + x = 14.753934086 Solving -42.5 + x = 14.753934086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '42.5' to each side of the equation. -42.5 + 42.5 + x = 14.753934086 + 42.5 Combine like terms: -42.5 + 42.5 = 0.0 0.0 + x = 14.753934086 + 42.5 x = 14.753934086 + 42.5 Combine like terms: 14.753934086 + 42.5 = 57.253934086 x = 57.253934086 Simplifying x = 57.253934086Subproblem 2
x + -42.5 = -14.753934086 Simplifying x + -42.5 = -14.753934086 Reorder the terms: -42.5 + x = -14.753934086 Solving -42.5 + x = -14.753934086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '42.5' to each side of the equation. -42.5 + 42.5 + x = -14.753934086 + 42.5 Combine like terms: -42.5 + 42.5 = 0.0 0.0 + x = -14.753934086 + 42.5 x = -14.753934086 + 42.5 Combine like terms: -14.753934086 + 42.5 = 27.746065914 x = 27.746065914 Simplifying x = 27.746065914Solution
The solution to the problem is based on the solutions from the subproblems. x = {57.253934086, 27.746065914}
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